not all of gravity is good to picture as waves. waves are just a part of the picture.
Like with electricity and magnetism, a charge sitting still exerts attraction or repulsion force on surrounding charge---but these are static forces, not waves
but if you move the charge back and forth in an antenna it makes spreading ripples of push-pull that are electromagnetic waves
so a star sitting still just exerts force on surroundings, simple Newtonian picture works, no waves.
but if you bring another star close to it and let it move around and around the first one, then it sends out spreading waves. because the companion star is now on right side and now on left, now nearer now farther, etc.
so it is like an electric charge going around in a circular antenna, making waves.
NOW WAVES CARRY ENERGY, they can do work, they can rock your boat or whatever, even generate electricity, so this orbiting system of two stars is sending out waves which carry away energy, WHERE DOES THAT ENERGY COME FROM.
It comes from the two stars SPIRALING IN CLOSER TO EACH OTHER because when they are closer together they have less potential energy
energy is the ability to do work. if you have a brick on a pulley you can get it to do work as it is lowered (make the rope turn something)======the higher up the brick is, the more potential it has to do work
the farther apart two stars are the more potential they have to do work if you could tie rope and lower them together with a pulley------so as they get closer energy goes somewhere.
in the case of the two NEUTRON STARS you read about they spiral in closer and closer and the potential energy that they lose by getting closer goes into two things: it goes into speeding them up, and it goes into making waves.
the good thing about neutron stars is they are small and compact so they can spiral in close to each other and get to going very fast, so they become efficient at making vigorous energetic waves-----not slow flabby waves that hardly carry any energy at all like ordinary orbital motions make. do the rate of energy loss was large enough to be measurable (by the increased speed as the orbit tightened).
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Now comes the exciting part. If you take the same two neutron stars they HAVE MORE MASS WHEN THEY ARE FARTHER APART THAN THEY DO WHEN THEY ARE CLOSER
that is just the standard thing that Einstein figured out in 1905 about a hot cannonball. He figured out that the same cannonball would weigh more if it was heated up. And it's true.
What determines the mass of the whole system is not only the individual masses of the component pieces but the energy that is stored in the WHOLE SYSTEM. So if you want to know the total mass of a two-star system it is not just adding up the mass of each star in isolation. That doesn't give the right answer. You have to include the energy embodied in their relationship----how far apart, how they are moving (potential and kinetic energy)
and with a cannonball you can't just add up the masses of the individual atoms, you have to take account of HEAT energy kinetic and potential, motion, bond energy too. Adding up the masses of the atoms measured in isolation only gives an approximate answer. the real mass includes everything.
so as the two neutron stars spiral in towards each other over 10 or 20 years, they radiate away some energy by gravity waves and then, since they are closer now they have less potential energy, and therefore they have less MASS as a combined two-star system. I think that is what you were asking about, the loss of mass. I don't think the loss of mass is an especially clear way to look at it. the main thing is the slow leakage loss of energy as they spiral in.
